There presently exists a need for efficient and compact sources of coherent radiation at a variety of visible and infrared wavelengths. Since efficient laser sources do not exist to meet this need, other mechanisms must be employed to generate coherent radiation at these wavelengths. Non-linear optical materials, which have non-linear optical susceptibilities that allow the material to generate radiation at a wavelength which differs from the wavelength of radiation applied to the material, present one way for achieving the desired visible and infrared sources. The unique properties of these materials can either be used to perform frequency conversion to generate harmonics of a given laser radiation, or to provide coupling between radiation of different frequencies to produce optically mixed sums or differences of the input radiation. By such frequency conversion techniques, the desired light can be generated from existing stable wavelength sources such as laser diodes or diode-pumped Nd:YAG lasers. For the purpose of frequency-doubling, a non-linear optical material may either be placed in the laser cavity (intracavity), or may be placed in an external cavity. In the intracavity case, the harmonic is resonated. In the external cavity case, either the fundamental or the harmonic, or both, may be resonated. Similarly, optical mixing may be performed either in an external cavity having two inputs to be summed or subtracted, or in an intracavity setting where the non-linear optical material is placed in the laser cavity, and the intracavity field of the laser is one of the "inputs".
One method for second harmonic generation (SHG) in an external cavity is described by Ashkin, et al, in "Resonant Optical Second Harmonic Generation and Mixing," IEEE Journal of Quantum Electronics, QE-2, pp. 106-124. The Ashkin article demonstrates the advantage of using an external resonant cavity to enhance the fields present in the doubling crystal, as compared to using a nonresonant single-pass technique. In Ashkin, the input light has ordinary polarization, and the generated second harmonic has extraordinary polarization. According to Ashkin, the presence of an external field at the second harmonic frequency will increase the power radiated by the non-linear crystal at the extraordinary polarization, assuming the external field is of the proper phase. Such an external field is effectively built up in a cavity that is resonant for the second harmonic in a technique referred to herein as the harmonic singly-resonant technique.
Ashkin also discusses making the external cavity resonant for the fundamental instead of the second harmonic, in what will be referred to herein as the fundamental singly-resonant technique. For this case, the conversion efficiency is improved as compared to the single-pass case since the power of the generated second harmonic is proportional to the square of the fundamental power passing through the crystal. Other literature examples of SHG using resonance of the fundamental include: "Efficient Second Harmonic Generation of a Diode-Laser Pumped CW Nd:YAG Laser Using Monolithic MgO:LiNbO.sub.3 External Resonant Cavities," by Kozlovsky, et al, in IEEE Journal of Quantum Electronics, 24, 913-919 (1988); "432-nm Source Based on Efficient Second-Harmonic Generation of GaAlAs Diode-Laser Radiation in a Self-Locking External Resonant Cavity," by Dixon, et al, in Optics Letters, 14, pp. 731-733 (1990); and "Second Harmonic Generation and Optical Stabilization of a Diode Laser in an External Ring Resonator," by Hemmerlich, et al, in Optics Letters, 15, pp. 372-374 (1990).
A more efficient technique for resonant SHG is discussed in "Doubly-resonant Second-Harmonic Generation in B-barium Borate," by Zimmerman, et al, Optics Communications, 71, pp. 229-234 (1989). According to this "doubly resonant" technique, the optical cavity is resonant for both the fundamental and the second harmonic, leading to greater output efficiencies for the output second harmonic. Further, such "double resonance" was used in an intracavity setting for SHG in "523-nm Composite-Cavity Internally-Doubled Close-Coupled LNP Cube Laser," Dixon et al, Postdeadline Papers, CLEO ' 89 (Optical Society of America, Washington , D.C., 1989) Paper CPDP37.
Second harmonic generation by the alternative singly-resonant techniques described above yield fair results, but only under limited circumstances. For example, the techniques only work well for non-linear materials having a significant non-linearity, generally in excess of 2 pm/volt. Second harmonic generation using singly-resonant techniques have been shown for 1064-nm Nd:YAG laser light using KTP or LiNbO.sub.3 as the non-linear crystal. Nonlinear materials capable of frequency-doubling lower frequency incident light (between 780 and 830 nm) are available, but have effective non-linearities and/or material properties which are too small for effective use in commercial devices. Materials capable of frequency-doubling of higher frequency light are also available, but either suffer from low non-linearities (KDP and LBO), or from a need to be heated to unduly high temperatures (300.degree. C. for lithium niobate) for red, but not for blue in order to achieve the required phase matching.
While the singly-resonant systems are limited by the practical material considerations described above, they are also limited by their optical properties. In the fundamental singly-resonant case where the cavity is made resonant for the fundamental, a high output power for the second harmonic is achieved since the output power goes as the square of the fundamental power through the crystal. Of course, to ensure maximum fundamental power through the crystal, the input fundamental beam must be spatially matched to the TEM.sub.00 mode at the frequency of the fundamental. Since the spatial quality of the input fundamental (e.g. as generated by a diode laser) is sometimes poor, expensive optics must be added to the SHG system to mode match the input beam to the cavity. Thus, the good power conversion achieved by resonating the fundamental is paid for by the need to add the optics necessary for mode matching.
The case of harmonic singly-resonant SHG, where the harmonic is resonated, is also limited by optical properties. Double refraction effects in the doubling crystal lead to Poynting vector walkoff for the generated second harmonic in the case of critical phase-matching. Accordingly, the second harmonic radiation resulting from a single pass through the doubling crystal is both non-Gaussian and displaced in the x-direction from the input Gaussian fundamental as discussed at page 110, et seq. in Ashkin. For this type of singly-resonant SHG, the cavity is made resonant for the second harmonic to provide power enhancement of the second harmonic generation in the crystal. The resulting resonating harmonic field is also displaced in the x-direction due to walkoff, but has a Gaussian profile. The non-Gaussian generated harmonic drives the various modes of the resonator. However, only that portion of the generated harmonic which is matched to the TEM.sub.00 mode of the harmonic will be resonantly enhanced. Thus, a power-coupling coefficient can be determined by considering the overlap between the generated harmonic and the TEM.sub.00 mode of the harmonic as a function of crystal length. This coefficient is calculated in Ashkin and is found to be around 35%. As for the higher order transverse modes present in the generated harmonic, these modes resonate at different frequencies than the TEM.sub.00 mode of the harmonic. As a result, they cannot resonate at the same time as the TEM.sub.00 mode, and thus do not contribute to the power-enhancement offered by having a cavity that is resonant for the second harmonic. Thus, this singly-resonant technique is limited because of the poor matching between the generated non-Gaussian harmonic and the TEM.sub.00 mode of the harmonic.
The doubly-resonant techniques of Zimmerman and Dixon, supra, offer advantages over both of these singly-resonant techniques. As recognized by Ashkin, the conversion efficiency of an external resonant frequency doubler can be significantly increased by resonating the fundamental input as well as the harmonic field of the external resonant cavity. The increased efficiency of harmonic conversion is maximized if the transmission of the output mirror at the wavelength of the second harmonic (or the sum or difference frequency for optical mixing) is equal to the intracavity losses at the output wavelength, and if certain conditions on the relative phases are met. The equality between transmission and intracavity losses can be realized by properly selecting the mirror transmissions. The phase and mode structure conditions are more difficult to meet.
The first requirement for a doubly-resonant system is that the round-trip phase shift experienced by both the fundamental and harmonic waves, as they return to the nonlinear crystal faces following reflection from the mirrors must be an integral multiple of 2 .pi.. For ring resonators, a similar condition holds at the front face of the non-linear crystal. This requirement can be met by: 1) varying the dispersion of the intracavity medium between the non-linear crystal and the mirrors; and/or 2) controlling the relative phase shifts of the fundamental and harmonic upon reflection from the cavity end mirrors; and/or 3) introducing a birefringent material between the crystal and the end mirrors. In the Zimmerman article, the angle of the non-linear crystal relative to the resonator, and its position along the axis of the cavity were used to control the phases at the crystal surfaces.
Even when the requirement of matched phase shifts in doubly-resonant cavities is met, the maximum benefit of output resonance can only be achieved if another condition is met. That condition requires that all of the output power produced in the non-linear crystal be frequency-matched to the resonator. For non-critically-phase-matched (where propagation of the generated light is along the optical axis of the crystal) harmonic generation and optical mixing, this condition is automatically fulfilled. For the critically-phase-matched case, however, Poynting vector walkoff creates a situation, similar to that of the harmonic singly-resonant case, in which the harmonic generated by the fundamental passing through the crystal is not spatially matched to the TEM.sub.00 mode of the harmonic (which is at the extraordinary polarization). Further, and also as in the harmonic singly resonant case, only that portion of the generated harmonic which is in the TEM.sub.00 mode of the harmonic is power enhanced, and the higher order transverse modes of the generated harmonic do not resonate and are thus not power-enhanced in the resonator. As discussed in Zimmerman, however, significant harmonic power is present in these higher order transverse modes. Thus, while doubly-resonant cavities offer advantages over singly-resonant ones, resonating the power contained in the higher order transverse modes would result in even more significant increases in harmonic output power.
Similar increases in output power could also be realized for both intracavity SHG and optical mixing if matching of the higher order transverse modes of the output to the TEM.sup.00 mode of that output could be achieved.